[HTML][HTML] Mean field analysis of neural networks: A central limit theorem

J Sirignano, K Spiliopoulos - Stochastic Processes and their Applications, 2020 - Elsevier
We rigorously prove a central limit theorem for neural network models with a single hidden
layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) …

Mean field analysis of neural networks: A law of large numbers

J Sirignano, K Spiliopoulos - SIAM Journal on Applied Mathematics, 2020 - SIAM
Machine learning, and in particular neural network models, have revolutionized fields such
as image, text, and speech recognition. Today, many important real-world applications in …

[HTML][HTML] Particle systems with a singular mean-field self-excitation. Application to neuronal networks

F Delarue, J Inglis, S Rubenthaler, E Tanré - Stochastic Processes and …, 2015 - Elsevier
We discuss the construction and approximation of solutions to a nonlinear McKean–Vlasov
equation driven by a singular self-excitatory interaction of the mean-field type. Such an …

Counterparty contagion in context: Contributions to systemic risk

JC Staum - Available at SSRN 1963459, 2012 - papers.ssrn.com
This article surveys models of counterparty contagion and their application in systemic risk
management, emphasizing the network of counterparty relationships. It addresses how …

Large portfolio asymptotics for loss from default

K Giesecke, K Spiliopoulos, RB Sowers… - Mathematical …, 2015 - Wiley Online Library
We prove a law of large numbers for the loss from default and use it for approximating the
distribution of the loss from default in large, potentially heterogeneous portfolios. The density …

-player games and mean-field games with absorption

L Campi, M Fischer - 2018 - projecteuclid.org
We introduce a simple class of mean-field games with absorbing boundary over a finite time
horizon. In the corresponding N-player games, the evolution of players' states is described …

An SPDE model for systemic risk with endogenous contagion

B Hambly, A Søjmark - Finance and Stochastics, 2019 - Springer
We propose a dynamic mean-field model for 'systemic risk'in large financial systems, derived
from a system of interacting diffusions on the positive half-line with an absorbing boundary at …

Risk analysis for large pools of loans

J Sirignano, K Giesecke - Management Science, 2019 - pubsonline.informs.org
Financial institutions, government-sponsored enterprises, and asset-backed security
investors are often exposed to delinquency and prepayment risk from large numbers of …

Systemic risk in interbanking networks

L Bo, A Capponi - SIAM Journal on Financial Mathematics, 2015 - SIAM
We develop a mean field model of interbanking borrowing and lending activities. Each bank
borrows from or lends to other counterparties at an idiosyncratic rate and is exposed to …

[HTML][HTML] Mean field games with absorption and common noise with a model of bank run

M Burzoni, L Campi - Stochastic Processes and their Applications, 2023 - Elsevier
We consider a mean field game describing the limit of a stochastic differential game of N-
players whose state dynamics are subject to idiosyncratic and common noise and that can …